This is a terrifyingly insecure cultural cringe of an exhibition, a pitiful act of obeisance by the National Gallery to popular culture, contemporary art and anything else it hopes might pull in a few young people. It’s like watching Dirk Bogarde at the end of Visconti’s film Death in Venice as his black hair dye drips down his face and he loses his last shred of dignity. Only this time it is a great institution that should know better than dyeing its hair, loosening its tie and trying to groove with the kids, which is making an unseemly spectacle of itself.

Those closing moments of Death in Venice are rendered unforgettable by the lush fourth movement of Mahler’s Fifth Symphony heaving its tones of nervous breakdown on the soundtrack. Sound and vision work sympathetic magic in cinema. Why not in an art gallery? Why shouldn’t we experience oil paintings with a soundtrack, especially in these times when sound artists win the Turner prize and cross art-form collaborations are, you know, cool?

Well, the reason why not, in a nutshell, is that great paintings do not need the emotional prompt of music and soundz to make them come alive. They are full of nuance, packed with surprise, and all you have to do is look at them. The optimum conditions for that are quiet rooms a bit like the National Gallery’s. Come to think of it, exactly like those. Instead, in this painfully pretentious exhibition, the silence is broken. Just like the first bird, Akseli Gallen-Kallela’s 1905 painting Lake Keitele is picked out at the start of the show by a spotlight in an otherwise empty space. Or rather, visually empty, for sound recordist Chris Watson accompanies it with birdsong and spooky cries. The effect is anodyne. What do these sounds add to the painting? I can already see that it depicts the great outdoors.

Through a black corridor into the next cloistered space, and eerie notes plucked from the haunted air by Turner prize-winner Susan Philipsz collide with no less a masterpiece than Hans Holbein’s The Ambassadors (1533). At first I found this even dafter than the first room, because the shaping of space by sound is more flamboyant. But soon I found Philipsz influencing where I put my eyes. Instead of the finery of the two men Holbein portrayed, her scraping sad strings pointed me straight towards the distorted skull that slashes across this disconcerting painting. I think I even saw the skull more clearly as a result of the music. The longer I stayed, the more Philipsz hacked into the melancholy of Holbein’s art.

So sound can, I admit, illuminate a painting. But it is a subtle and fragile relationship, and Philipsz is the only artist here who carries it off. Most of the other interventions are irrelevant or mind-numbing. Janet Cardiff and George Bures Miller have put together an array of aural and visual distractions that just about succeed in totally ruining Antonello da Messina’s jewel of a Renaissance painting Saint Jerome in his Study. This is one of my favourite paintings in the National Gallery. I love its tranquil, mysterious space. Here, that space is rendered in a leaden 3D model and an aimless array of sounds including cliched medieval music. Dig that monastic vibe. The painting hangs glumly in a corner, intimidated by this nonsense.

Then there are two composers who have installed bits of classical music against Cézanne’s Bathers and the Wilton Diptych. These two rooms reminded me of the soundtracks of television documentaries. Here’s a bit of semi-discordant piano for Cézanne’s modernism. Here’s a choir for that medieval feel. The juxtapositions are not quite as crude as that, but the music collides irritatingly with the paintings one minute, then cornily over-emphasises them the next, without ever achieving symbiosis. I would rather see them in old-fashioned silence, thanks.

electro-dancemeister Jamie xx to save the show. Can he pull it off? Well at least you can tap your feet to his beats. He has also picked a painting that his ethereal mixes can actually illuminate. Theo van Rysselberghe’s Coastal Scene (c 1892) is a pixelated constellation of light, a silvery blue vision that, as you get closer, fragments into blips of perception. Beats and pulses. The music suits it well. Or is this just using a painting as a high-class pop video? You can do it yourself on YouTube. And that’s it. There are only six paintings in this exhibition. Admission costs £10. It is an experiment that does the National Gallery no credit at all. Philipsz is really the only artist worth the admittance fee. A one-off installation by her would have been a fine free summer show. Instead, this is a depressing admission by the National Gallery that it is bored by its duty to show old art. It wants to put flowers in its hair and do Glasto next year. It wants to air-kiss pop culture. I have just one word for this daft exhibition. Shush!

Soundscapes is at the National Gallery, London, from 8 July to 6 September.